Regatta, Inc., has six-year bonds outstanding that pay an 8.25 percent coupon rate. Investors buying the bond today can expect to earn a yield to maturity of 6.875 percent. How much will you be willing to pay for Regatta's bond today

Price of bond = $1,065.79

Explanation:

The price of a bond is the present value of the expected interest payments plus the present value of the redemption value (RV)

Price of a bond = PV of Interest payment + PV of RV

PV of Interest payment

Interest payment = 8.25% * 1000 = 82.5

PV of interest payment

PV = A * (1 - (1+r) ^ (-n) / r

A - interests payment, r - yield to maturity, r - year to maturity

A - 82.5, r - 6.875%, n - 6

PV of interest = 82.5 * (1 - (1.06875) ^ (-6)) / 0.06875 = 394.7615956

PV of RV

PV = RV * (1+r) ^ (-n)

RV - Redemption value, r - yield to maturity, n - year to maturity

PV of RV = 1000 * (1.06875) ^ (-6) = 671.0320037

Price = 394.76 + 671.03

Price = $1,065.79

Price of bond = $1,065.79

Explanation:

Calculating the price of the bond, we use

Price of a bond = PV of Interest payment + PV of RV

Let's calculate the interest payment first as;

Interest payment = 8.25% * 100 = 82.5

PV of interest payment is calculated using this formula

PV = A * (1 - (1+r) ^ (-n) / r

Where

A = interests payment = 82.5

r = yield to maturity = 6.875%

n = year to maturity = 6

Substituting the values, we

PV of interest = 82.5 * (1 - (1.06875) ^ (-6)) / 0.06875

PV of interest = 394.7615956

PV of Redemption value is been calculated using this formula

PV = RV * (1+r) ^ (-n)

Where;

RV = Redemption value = 1000

r = yield to maturity = 0.06875

n = year to maturity = 6

Substituting the values in to the formula

PV of Redemption value = 1000 * (1.06875) ^ (-6)

PV of Redemption value = 671.0320037

Finally

Price of bond = PV of Interest payment + PV of RV

Price of bond = 394.76 + 671.03

Price of bond = $1,065.79